NCERT Solutions Class 11 Maths Chapter 1 Sets Exercise 1.3 Solutions 

CBSE CLASS XII Related Questions

  • 1.
    Find : \[ \int \frac{2x+1}{\sqrt{x^2+6x}}\,dx \]


      • 2.

        The probability of hitting the target by a trained sniper is three times the probability of not hitting the target on a stormy day due to high wind speed. The sniper fired two shots on the target on a stormy day when wind speed was very high. Find the probability that 
        (i) target is hit. 
        (ii) at least one shot misses the target. 


          • 3.
            Find the sub–interval of \((0,\pi)\) in which the function \[ f(x)=\tan^{-1}(\sin x-\cos x) \] is increasing and decreasing.


              • 4.
                Evaluate : \[ \int_{-\frac{\pi}{6}}^{\frac{\pi}{3}}(\sin|x|+\cos|x|)\,dx \]


                  • 5.

                    Smoking increases the risk of lung problems. A study revealed that 170 in 1000 males who smoke develop lung complications, while 120 out of 1000 females who smoke develop lung related problems. In a colony, 50 people were found to be smokers of which 30 are males. A person is selected at random from these 50 people and tested for lung related problems. Based on the given information answer the following questions: 

                    (i) What is the probability that selected person is a female? 
                    (ii) If a male person is selected, what is the probability that he will not be suffering from lung problems? 
                    (iii)(a) A person selected at random is detected with lung complications. Find the probability that selected person is a female. 
                    OR 
                    (iii)(b) A person selected at random is not having lung problems. Find the probability that the person is a male. 
                     


                      • 6.
                        Obtain the value of \[ \Delta = \begin{vmatrix} 1 + x & 1 & 1 \\ 1 & 1 + y & 1 \\ 1 & 1 & 1 + z \end{vmatrix} \] in terms of \(x, y, z\). Further, if \(\Delta = 0\) and \(x, y, z\) are non–zero real numbers, prove that \[ x^{-1} + y^{-1} + z^{-1} = -1 \]

                          CBSE CLASS XII Previous Year Papers

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